How do I create an AI for a two-players board game?
Assuming it is a turn-based game and, for each turn, there's an optimal choice that will lead to the winning state (zero-sum), you can basically simplify the question to "What is the optimal sequences of moves for me to win, considering the current situation that is presented on the board?". So you will need to perform your algorithm every turn as the optimal sequence will change when the board changed.

There's a relatively reliable AI algorithm that's being implemented to win games like chess, backgammon, etc. The technique is called minimax. In summary, minimax is simply a search algorithm to minimize the other player's score, while maximizing your score.

One of the problems you will encounter is that the search tree becomes so wide as we search through deeper parts of the tree, so it is essential to also implement alpha-beta pruning to cut down the amount of search. In general, alpha-beta pruning is simply eliminating branches that are very unlikely to be the optimal choice (in terms of score) thus reducing the number of searches to speed up the algorithm.